Coulomb, Tresca and Coulomb-Tresca friction models used in analytical analysis for rolling process of external spline

Abstract

The plastic deformation during external spline rolling process (ESRP) is concentrated in the superficial area of workpiece. The numerical simulation for full 3D spline rolling process is time-consuming, and experimental measure during the rolling process is also difficult, and there is no clear physical meaning between results and parameters. The analytical models for ESRP have been modeled by slip-line field method (SLFM) with Coulomb friction model (CFM), Tresca friction model (TFM) and Coulomb-Tresca friction model (CTFM), respectively. The SLFM models can represent the influence of geometrical and frictional parameters on the ESRP. The slip line fields of ESRP under different friction models all contain 3 slip-line sub-regions for workpiece only with circular dedendum and all contain 5 slip-line sub-regions for workpiece with involute flank. Compared with experimental and numerical results, the error of SLFM (slip-line field method) result such as undeformed zone of the workpiece is less than 10 % between SLFM results and the experimental and FEM results. The error between SLFM and FEM for normal stress on contact surface is less than 10 %. The geometrical parameter and friction condition have an important influence on the applicability of CTFM. CTFM only works in the rolling process with small pressure angle (such as 14.5° for gear) and friction condition (0.7<m<0.8) between lubrication and dry friction; and for other cases, the CTFM degenerates into a TFM. The developed SLFM model in this study can provide a basis for studying deformation mechanism, rapidly determining reasonable parameter range, and simplifying finite element model of spline or gear rolling process. The results in this study also provided reference for selection of friction model in finite element analyses of complex profile rolling.